Hour Exam 3 Review

Exam is Wednesday at 7:00 pm

Remember extra office hours

A ladder of weight 60 N leans against a frictionless wall

at an angle of q = 70o as shown in the figure. Friction between the

floor and the ladder keeps it from slipping

. What is the magnitude of the force of friction, Ff, between the floor and the ladder?

a. Ff = 5.0 N

b. Ff = 11. N

c. Ff = 15. N

d. Ff = 29. N

e. Ff = 60 N

2. If the angle of the ladder were decreased from 70o to 50

o, the force of friction required

to keep the ladder from slipping would

a. increase

b. decrease

c. remain the same

Consider a student rotating on a stool with angular speed , holding weights in her

outstretched hands. If she drops one of the weights to the ground, her angular speed

will

a. increase

b. stay the same

c. decrease

4. Now consider a student rotating on a stool with angular speed with no weights in

her hands. Suppose someone drops (vertically) a small weight into her horizontally

outstretched hand. Her angular speed will

a. increase

b. stay the same

c. decrease

A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular

bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely

about a pivot at its center. The gum sticks to the end of the bar and the angular speed of

the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of

gum is a point particle and assume that the pivot is frictionless.

(You do not have to worry about gravity in this problem)

5. What is the magnitude of the angular momentum of the gum with respect to the

pivot before it collides with the bar?

a. 0 kg m2 /s

b. 0.48 kg m2 /s

c. 1.12 kg m2 /s

A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular

bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely

about a pivot at its center. The gum sticks to the end of the bar and the angular speed of

the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of

gum is a point particle and assume that the pivot is frictionless.

(You do not have to worry about gravity in this problem)

6. What is the angular momentum of the gum with respect to the pivot after it collides

with bar?

a. 0.29 kg m2 /s

b. 0.48 kg m2 /s

c. 1.12 kg m2 /s

A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular

bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely

about a pivot at its center. The gum sticks to the end of the bar and the angular speed of

the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of

gum is a point particle and assume that the pivot is frictionless.

(You do not have to worry about gravity in this problem)

7. What is the mass of the bar?

a. 1.7 kg

b. 2.0 kg

c. 2.3 kg

d. 3.1 kg

e. 5.2 kg

The axle of a spinning disk of mass m is placed upon a single fixed support as shown

below. The disk’s angular velocity vector is indicated in the figure, as is the

gravitational force on the disk.

8. Which of the following figures accurately shows the motion of the spinning disk?

a. As viewed from above, the disk precesses clockwise:

b. As viewed from above, the disk precesses counter-clockwise.

c. The disk does not fall and does not precess.

L pivot

mg

pivot

mg

pivot

mg

pivot

mg

A skater spins about a fixed point on the ice. She begins with her arms extended and an

initial angular velocity 0. She then pulls her arms in to her body. After her arms are

pulled to her body, she spins with an angular velocity f. Throughout the time she is

spinning, no external forces are acting in the horizontal plane.

9. How do the magnitudes of the initial and final angular velocities compare?

a. 0 > f

b. 0 = f

c. 0 < f

10. Which one of the following statements is true?

a. The angular momentum of the skater remains constant.

b. The moment of inertia of the skater remains constant.

c. Both the angular momentum and the moment of inertia of the skater change.

11. The kinetic energy of the skater

a. increases because the skater does work.

b. decreases because the skater does work.

c. stays the same because the skater does no work.

A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with

a frictionless pivot and a string as shown in the diagram above. The initial angle

of the rod with respect to the wall, , is 39. The string is then cut. The moment

of inertia of a rod about an axis through one end is 1/3ML2.

12. What is the angular acceleration of the rod, , immediately after the string

is cut?

a. = 1.75 rad/s2

b. = 3.09 rad/s2

c. = 4.92 rad/s2

d. = 6.17 rad/s2

e. = 7.84 rad/s2

13. What is the angular velocity of the rod when it is horizontal (=90)

a. 1.4 rad/sec

b. 3.1 rad/sec

c. 3.9 rad/sec

A disk of radius R, mass M, and moment of inertia I = (1/2)MR2 rolls without slipping

down an incline and onto a horizontal table. The disk then continues to the right and goes

up a frictionless ramp. The disk starts at rest at a height h above the table, as shown

14. What is the speed of the center of mass of the disk when it reaches the bottom of the

ramp?

a. gh2

b. 3

4 gh

c. 7

10 gh

d. gh

e. Mgh

15. What is the maximum height above the table that the disk reaches on the frictionless ramp?

a. less than h

b. h

c. greater than h

A disk has mass M = 1.0 kg and radius, R = 0.1 m is

free to rotate about a fixed axle through its center.

Since the axle is fixed, the center of mass of the disk

does not move. The disk is initially not rotating. A

student wraps a string 12 times around the perimeter

of the disk and then pulls the string with a constant

force of F = 1.0 N, as shown in the figure below

16. The student pulls on the string until it is completely unwound, and the string does

not slip on the disk as it is pulled. After the string has unwound, what is the angular

speed of the disk :

a. = 6.3 radians/sec

b. = 17.6 radians/sec

c. = 26.4 radians/sec

d. = 32.8 radians/sec

e. = 54.9 radians/sec

A disk has mass M = 1.0 kg and radius, R = 0.1 m is

free to rotate about a fixed axle through its center.

Since the axle is fixed, the center of mass of the disk

does not move. The disk is initially not rotating. A

student wraps a string 12 times around the perimeter

of the disk and then pulls the string with a constant

force of F = 1.0 N, as shown in the figure below

17. Now suppose the student repeats the experiment, this time wrapping the string

around the perimeter of the disk 6 times and pulling the string with a constant force of

F = 2.0 N. As before, the disk is initially not rotating. How does the angular speed of

the disk after the string unwinds, , compare to found in the previous problem?

a. <

b. =

c. >

F= 15 N

M

r

Top

View ACM =2.1 m/s2

R Side

View

F

Frictionless Table

A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is

pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a

vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its

inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is

observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of

inertia for the spool is given by 1/2MR2)

18. What is the mass of the disk M?

a. 2.75 kg

b. 5.28 kg

c. 7.14 kg

F= 15 N

M

r

Top

View ACM =2.1 m/s2

R Side

View

F

Frictionless Table

A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is

pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a

vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its

inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is

observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of

inertia for the spool is given by 1/2MR2)

19. What is the angular acceleration of the disk ?

a. 2.8 rad/s2

b. 4.7 rad/s2

c. 8.4 rad/s2

d. 3.3 rad/s2

e. 7.1 rad/s2

A Physics 211 student is out shoveling snow in the driveway. At one point he holds

the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without

moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the

right, and the center of mass of the snow is 0.5 meters further to the right as shown

in the figure below. Gravity acts in the –y direction.

20. Assuming the shovel is massless, what is the y-component Fy of the force

that his left hand exerts on the shovel?

a. Fy = –35 N

b. Fy = –10 N

c. Fy = 0 N

d. Fy = 10 N

e. Fy = 35 N

A Physics 211 student is out shoveling snow in the driveway. At one point he holds

the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without

moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the

right, and the center of mass of the snow is 0.5 meters further to the right as shown

in the figure below. Gravity acts in the –y direction.

21. Now suppose that the handle of the shovel has a mass of 1 kg, uniformly distributed

along its 1.2 meter length. Taking into account the mass of the handle, the magnitude of the

force of the student’s left hand on the end of the shovel’s handle will

a. increase.

b. decrease.

c. stay the same.

M

m1

m2 a =g/3

T1=170N T2=255N

R

Two blocks are suspended over a pulley by a string of negligible mass as shown below. The

block on the left has a mass of m1, and the block on the right has mass m2. The pulley is a

uniform solid cylinder with mass M and radius R. The block on the right has a downward

acceleration equal to 1/3 the acceleration due to gravity. The tension in the string supporting

the mass on the left is T1 = 170N and the tension in the string supporting the mass on the right

is T2 = 255N. The string does not slip on the pulley.

22. What is the mass, m2, of the block on the right?

a. m2 = 43 kg

b. m2 = 39 kg

c. m2 = 26 kg

23. What is the mass, M, of the pulley?

a. M = 14 kg

b. M = 27 kg

c. M = 39 kg

d. M = 46 kg

e. M = 52 kg

24. A judge’s gavel has a mass of 0.7 kg and has a moment of inertia of 0.10 kg m2

around an axis through its center of mass, perpendicular to the paper in the drawing

above. The distance between the center of mass of the gavel and the end of the handle

is 30 cm. What is the moment of inertia of the gavel around an axis through the end of

the handle, perpendicular to the paper?

a. 0.05 kg m2

b. 0.10 kg m2

c. 0.16 kg m2

d. 0.20 kg m2

e. 0.31 kg m2